Advection is a transport mechanism of a substance or conserved property by a fluid, due to the fluid's bulk motion. An example of advection is the transport of pollutants or silt in a river by bulk water flow downstream. The advection diffusion equation is a combination of the diffusion and convection equations. It describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion, and convection.
Minimax (also referred to as MinMax) is a decision rule used in decision theory, game theory, statistics, and philosophy for minimizing the possible loss for a worst case (maximum loss) scenario. This decision rule is often applied to general decision making in the presence of uncertainty.
Planning remediation strategies, for example, in environmental contamination, simulated transport in an advection diffusion process is relied upon for predicting, or forecasting, transport trajectories. In such applications, the choice of domain, or environment, for the numerical simulation is an important component in prediction abilities of an operating model. For example, the choice of domain for the numerical simulation is a key point for the correctness of the prediction system. That is, a small domain may deteriorate the prediction, while a large domain may be computationally unfeasible.
The generation of domains and sub-domains is generally determined by the user of the system, or by the domain expert that is doing the simulation. Typically, the mesh generated covers the physical domain that is to be simulated and the sub-domains are consequently generated depending upon the computational facilities available to the user. The only constraint is that the sub-domains must not overlap.